By that argument, playing with a frisbee is also fight-related. That's a pretty distant reach. And the reactions needed (and type of eye-hand coordination, for that matter) for swinging a bat isn't the same as what's needed for dealing with a punch. That link seems about as direct as the link between getting a step to fall where you want in kata and being able to take a step of the right length to close distance in a fight.
So, because it's not used in soccer, it must not be useful for fighting? Seriously, it's been said that it's not a direct application, but one attribute that can be viewed. You're very fixated on the single point of a kata ending where it started. There are some concepts that can be related to this (nobody claimed mobility was one, that I can recall) control, and some of them are even related to fighting. But it's still just one small point in the idea of using kata.
I made the point earlier that arguing about a point in kata and saying it's flawed because it doesn't have a strong link to fighting misses that maybe that point isn't meant to be about fighting. You keep coming back to how a given point isn't well related to fighting. That seems to either ignoring my point, or arguing that it must be about fighting. Even if we just said kata is a basic mobility movement training exercise (like non-martial tai chi in the park), I wouldn't see that as a bad thing - so long as people understand what they're doing and what they will (and won't) get out of it. And if they want to waltz in their MA classes, that might serve the same purpose.